Strongly correlated quantum many-body systems, i.e. those in which quantum correlations play an important role, exhibit many exciting phenomena such as superconductivity, the fractional quantum Hall effect, or topological order. In this lecture, we will discuss how to use quantum information concepts - in particular the theory of entanglement - to better understand those systems.

The focus of the lecture will be on Tensor Network methods (in particular Matrix Product States, PEPS, and MERA) which form a framework to describe correlated quantum many-body systems by capturing their entanglement properties, and which have proven to be very useful both analytically and numerically (e.g. in the Density Matrix Renormalization Group [DMRG] method). However, we will also discuss other quantum information aspects of quantum many-body systems, such as aspects of topological order, or the propagation of information and Lieb-Robinson bounds.

While there will be certain “core topics” in the lecture, the exact selection of topics - in particular also the balance between analytical and numerical aspects - will be adjusted depending on the interest of the audience.

Prerequisites:

A thorough background in quantum mechanics is required. Familiarity with topics in quantum many-body physics and quantum information theory is not necessary, but certainly useful.